{"id":464,"date":"2026-05-05T04:47:11","date_gmt":"2026-05-05T04:47:11","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thcs-thpt-nguyen-khuyen-tphcm\/"},"modified":"2026-05-05T07:20:13","modified_gmt":"2026-05-05T07:20:13","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thcs-thpt-nguyen-khuyen-tphcm","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thcs-thpt-nguyen-khuyen-tphcm\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM<\/strong> \u2013 t\u1ed5ng h\u1ee3p d\u1ea1ng \u0111\u1ec1 thi th\u1eed m\u00f4n To\u00e1n cho c\u00e1c b\u1ea1n h\u1ecdc sinh 12 c\u00f3 th\u1ec3 t\u1ef1 tin h\u01a1n trong vi\u1ec7c \u00f4n t\u1eadp v\u00e0 b\u1ee9c ph\u00e1 trong k\u00ec thi quan tr\u1ecdng s\u1eafp \u0111\u1ebfn. C\u1ea5u tr\u00fac \u0111\u1ec1 thi chu\u1ea9n theo quy \u0111\u1ecbnh c\u1ee7a b\u1ed9 GD&\u0110T v\u1edbi nhi\u1ec1u d\u1ea1ng b\u00e0i t\u1eadp b\u00e1m s\u00e1t v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc. T\u00ecm hi\u1ec3u chi ti\u1ebft n\u1ed9i dung c\u1ee7a \u0111\u1ec1 thi th\u1eed v\u00e0 b\u1eaft \u0111\u1ea7u \u00d4n Thi<\/a><\/strong> ngay nh\u00e9!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM<\/strong><\/h2>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM<\/strong> chia l\u00e0m 2 m\u1ee5c: \u0110\u1ec1 thi th\u1eed v\u00e0 \u0110\u00e1p \u00e1n chi ti\u1ebft. \u0110\u00e2y l\u00e0 ch\u00eca kh\u00f3a gi\u00fap c\u00e1c b\u1ea1n h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 nh\u1ea5t. \u0110\u1ec1 thi c\u00f3 c\u1ea5u tr\u00fac g\u1ed3m 3 ph\u1ea7n ch\u00ednh v\u00e0 c\u00f3 n\u1ed9i dung nh\u01b0 sau:<\/p>\n

Ph\u1ea7n 1 \u2013 C\u00e1c c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ( 12 c\u00e2u )<\/strong><\/span><\/p>\n

C\u00f3 4 \u0111\u00e1p \u00e1n A, B, C, D. B\u1ea1n c\u1ea7n ch\u1ecdn ra \u0111\u00e1p \u00e1n ch\u00ednh x\u00e1c nh\u1ea5t t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u00e2u h\u1ecfi c\u1ee7a \u0111\u1ec1. Ch\u1ee7 y\u1ebfu ph\u1ea7n n\u00e0y ki\u1ebfn th\u1ee9c s\u1ebd ph\u00e2n b\u1ed5 c\u00e1c n\u1ed9i dung v\u1ec1 nguy\u00ean h\u00e0m, Logarit, s\u1ef1 \u0111\u1ed3ng bi\u1ebfn ngh\u1ecbch bi\u1ebfn c\u1ee7a h\u00e0m s\u1ed1,\u2026. Tham kh\u1ea3o c\u00e1c c\u00e2u h\u1ecfi sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1: Cho c\u1ea5p s\u1ed1 c\u1ed9ng (u_n) v\u1edbi u\u2081 = -1, u\u2082 = 4 . Gi\u00e1 tr\u1ecb c\u1ee7a u\u2085 b\u1eb1ng:
\n\\begin{align*}
\n\\text{A. } 9 \\quad\\quad \\text{B. } -16 \\quad\\quad \\text{C. } 7 \\quad\\quad \\text{D. } -8
\n\\end{align*}<\/p>\n

\"\"<\/p>\n

C\u00e2u 2: Cho h\u00e0m s\u1ed1 y = (ax + b)\/(cx + d) v\u1edbi a, b, c, d in mathbbR c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd. M\u1ec7nh \u0111\u1ec1 n\u00e0o \u0111\u00fang?
\n\\begin{align*}
\n\\text{A. } y\u2019 > 0, \\forall x \\ne 1 \\quad\\quad
\n\\text{B. } y\u2019 > 0, \\forall x \\in \\mathbb{R} \\quad\\quad
\n\\text{C. } y\u2019 < 0, \\forall x \\in \\mathbb{R} \\quad\\quad
\n\\text{D. } y\u2019 < 0, \\forall x \\ne 1
\n\\end{align*}<\/p>\n

Ph\u1ea7n 2 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m \u0111\u00fang sai ( 4 c\u00e2u )<\/strong><\/span><\/p>\n

Tr\u00edch m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 thi th\u1eed nh\u01b0 sau:<\/p>\n

C\u00e2u 4: X\u00e1c su\u1ea5t \u0111\u1ec3 c\u00f4ng ty X thu\u00ea m\u1ed9t trong hai c\u00f4ng ty v\u1ec7 tinh A v\u00e0 B t\u01b0 v\u1ea5n l\u1ea7n l\u01b0\u1ee3t l\u00e0 0,4 v\u00e0 0,6. Theo kinh nghi\u1ec7m, kh\u1ea3 n\u0103ng X ph\u00e1t sinh th\u00eam chi ph\u00ed khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u01b0 v\u1ea5n c\u1ee7a c\u00f4ng ty A v\u00e0 B l\u1ea7n l\u01b0\u1ee3t l\u00e0 0,05 v\u00e0 0,03.<\/p>\n

a) X\u00e1c su\u1ea5t \u0111\u1ec3 X c\u00f3 ph\u00e1t sinh th\u00eam chi ph\u00ed khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u01b0 v\u1ea5n l\u00e0 0,038<\/p>\n

b) Bi\u1ebft X c\u00f3 ph\u00e1t sinh th\u00eam chi ph\u00ed khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u01b0 v\u1ea5n. X\u00e1c su\u1ea5t \u0111\u1ec3 X thu\u00ea c\u00f4ng ty A t\u01b0 v\u1ea5n l\u00e0 0,4737<\/p>\n

c) Bi\u1ebft X c\u00f3 ph\u00e1t sinh th\u00eam chi ph\u00ed khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u01b0 v\u1ea5n. X\u00e1c su\u1ea5t \u0111\u1ec3 X thu\u00ea c\u00f4ng ty B t\u01b0 v\u1ea5n l\u00e0 0,5263<\/p>\n

d) Bi\u1ebft X kh\u00f4ng ph\u00e1t sinh th\u00eam chi ph\u00ed khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u01b0 v\u1ea5n. X\u00e1c su\u1ea5t \u0111\u1ec3 X thu\u00ea c\u00f4ng ty A t\u01b0 v\u1ea5n l\u00e0 0,395<\/p>\n

Ph\u1ea7n 3 \u2013 C\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn ( 6 c\u00e2u )<\/strong><\/span><\/p>\n

Ph\u1ea7n n\u00e0y chi\u1ebfm th\u1eddi gian nh\u1ea5t trong qu\u00e1 tr\u00ecnh c\u00e1c b\u1ea1n gi\u1ea3i \u0111\u1ec1. L\u01b0u \u00fd n\u00ean \u00f4n t\u1eadp ki\u1ebfn th\u1ee9c th\u1eadt v\u1eefng v\u00e0 gi\u1ea3i b\u00e0i t\u1eadp d\u1ea1ng n\u00e0y th\u1eadt nhi\u1ec1u \u0111\u1ec3 n\u00e2ng cao t\u01b0 duy logic nh\u00e9.<\/p>\n

C\u00e2u 1: Trong m\u1ed9t cu\u1ed9c thi v\u1ec1 \u201cb\u1eefa \u0103n dinh d\u01b0\u1ee1ng\u201d, ban t\u1ed5 ch\u1ee9c y\u00eau c\u1ea7u \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o l\u01b0\u1ee3ng dinh d\u01b0\u1ee1ng h\u1eb1ng ng\u00e0y th\u00ec m\u1ed7i gia \u0111\u00ecnh c\u00f3 4 th\u00e0nh vi\u00ean c\u1ea7n \u00edt nh\u1ea5t 900 \u0111\u01a1n v\u1ecb pr\u00f4t\u00eain v\u00e0 400 \u0111\u01a1n v\u1ecb lip\u00edt trong th\u1ee9c \u0103n h\u1eb1ng ng\u00e0y. M\u1ed7i 1 (kg) th\u1ecbt b\u00f2 ch\u1ee9a 800 \u0111\u01a1n v\u1ecb pr\u00f4t\u00eain v\u00e0 200 \u0111\u01a1n v\u1ecb lip\u00edt, 1 (kg) th\u1ecbt heo ch\u1ee9a 600 \u0111\u01a1n v\u1ecb pr\u00f4t\u00eain v\u00e0 400 \u0111\u01a1n v\u1ecb lip\u00edt. Bi\u1ebft r\u1eb1ng ng\u01b0\u1eddi n\u1ed9i tr\u1ee3 ch\u1ec9 \u0111\u01b0\u1ee3c chi t\u1ed1i \u0111a 200 ngh\u00ecn \u0111\u1ed3ng \u0111\u1ec3 mua th\u1ecbt. Bi\u1ebft r\u1eb1ng: 1 (kg) th\u1ecbt b\u00f2 gi\u00e1 200 ngh\u00ecn \u0111\u1ed3ng, 1 (kg) th\u1ecbt heo gi\u00e1 100 ngh\u00ecn \u0111\u1ed3ng. Ng\u01b0\u1eddi n\u1ed9i tr\u1ee3 n\u00ean mua x (kg) th\u1ecbt b\u00f2 v\u00e0 y (kg) th\u1ecbt heo \u0111\u1ec3 ph\u00ed th\u1ea5p nh\u1ea5t cho kh\u1ea9u ph\u1ea7n th\u1ee9c \u0103n m\u00e0 v\u1eabn \u0111\u1ea3m b\u1ea3o ch\u1ea5t dinh d\u01b0\u1ee1ng. Khi \u0111\u00f3 h\u00e3y t\u00ecm x + 2y .<\/p>\n

C\u00e2u 2: M\u1ed9t b\u1ec3 c\u00e1 \u0111\u00e1y n\u01b0\u1edbc c\u00f3 d\u1ea1ng h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.EFGH v\u1edbi AB = 6 (dm), AD = 8 (dm) v\u00e0 c\u1ea1nh b\u00ean b\u1eb1ng 10 (dm) . M\u1ed9t ch\u00fa c\u00e1 con b\u01a1i theo nh\u1eefng \u0111o\u1ea1n th\u1eb3ng t\u1eeb \u0111i\u1ec3m G \u0111\u1ebfn ch\u1ea1m m\u1eb7t \u0111\u00e1y c\u1ee7a h\u1ed3, r\u1ed3i t\u1eeb \u0111i\u1ec3m \u0111\u00f3 b\u01a1i \u0111\u1ebfn v\u1ecb tr\u00ed \u0111i\u1ec3m M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AF , \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh h\u00f3a nh\u01b0 h\u00ecnh. \u0110\u1ec3 \u0111\u01b0\u1eddng \u0111i ng\u1eafn nh\u1ea5t th\u00ec ch\u00fa c\u00e1 b\u01a1i \u0111\u1ebfn \u0111i\u1ec3m d\u01b0\u1edbi \u0111\u00e1y h\u1ed3 c\u00e1ch BA v\u00e0 BC nh\u1eefng \u0111o\u1ea1n b\u1eb1ng a v\u00e0 b . Khi \u0111\u00f3 t\u1ed5ng D = 3a + 6b bao nhi\u00eau?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM<\/strong><\/h2>\n

M\u1eddi qu\u00fd th\u1ea7y c\u00f4 v\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh t\u1ea3i ngay \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THCS & THPT Nguy\u1ec5n Khuy\u1ebfn TPHCM<\/strong> v\u00e0 \u0111\u00e1p \u00e1n chi ti\u1ebft \u0111\u1ec1 thi thpt to\u00e1n<\/a> <\/span>qua \u0111\u01b0\u1eddng link sau \u0111\u00e2y! V\u00e0 h\u00e3y chu\u1ea9n b\u1ecb m\u1ed9t ti\u1ebfn tr\u00ecnh \u00f4n t\u1eadp khoa h\u1ecdc \u0111\u1ec3 chinh ph\u1ee5c \u0111i\u1ec3m s\u1ed1 cao nh\u1ea5t trong k\u00ec thi t\u1ed1t nghi\u1ec7p THPT s\u1eafp \u0111\u1ebfn.<\/p>\n